Question

A uniform thin rod of length 4a+2πa and mass 4m+2πm is bent and
fabricated to form a square surrounded by four semicircles
The M. I. of
this frame about an axis passing through center and perpendicular to plane​

Answer 1

Answer:

Explanation:

Given A uniform thin rod of length 4a+2πa and mass 4m+2πm is bent and

fabricated to form a square surrounded by four semicircles

The M. I. of

this frame about an axis passing through center and perpendicular to plane

Given mass of each side of square is m

Length of each side of square is a

Mass of each semi-circle = π m / 2

Radius of each semi-circle = a/2

Now moment of inertia of square

          = 4 (m a^2 / 12 + m a^2 / 4)  

          = 4(4a^2 / 12 m)

          = 4/3 ma^2  

Now moment of inertia of semicircle

      = 4 (a^2 / 4 x πm / 2 + πm / 2 x a^2 / 4)

     = π m a^2

Now total moment of inertia will be

I = 4/3 ma^2 + πma^2

I = 4 + 3π / 3 ma^2